1. Melt butter in a large stockpot over medium heat until foamy. Add carrots, onion, and celery. Season with 1/4 teaspoon salt and pepper. Sauté until onions are translucent, about 6 to 8 minutes. Add garlic, and sauté until fragrant, about 2 minutes.

3. Slowly pour in vegetable stock, whisking until smooth. Add crushed tomatoes and remaining 1/2 teaspoon salt, whisking to combine. Cover, and increase heat to high; bring to a boil. Reduce heat to medium-low, and simmer for 40 minutes, occasionally whisking and scraping bottom of pot to keep from scalding.

4. Meanwhile, combine brown sugar and vinegar in a small saucepan over medium heat. Simmer, stirring occasionally, until mixture is syrupy and reduced by half, about 10 minutes. Set aside.

5. Add cream and basil to soup, stirring to combine. Add reserved sugar-vinegar mixture, stirring to combine. Purée soup in the pot using a hand blender; alternatively, puree soup in batches with a regular blender. Pour pureed soup through a fine-mesh sieve into a separate stockpot or serving bowl.